mersenneforum.org (https://www.mersenneforum.org/index.php)
-   Aliquot Sequences (https://www.mersenneforum.org/forumdisplay.php?f=90)
-   -   Odds and ends....and class records (https://www.mersenneforum.org/showthread.php?t=11673)

 rodac 2009-09-20 00:15

Hello :smile:

I have seen that the sequences 102072 and 84822 merge on the high number 8001424452.

Is it the highest merge or do higher merges exist for the sequences beginning under 10^6 ? :mellow:

 10metreh 2009-09-26 09:17

I think this (from 561528) deserves a mention:

[code] 1036 . 71094710687983183844919102767194019196508346229508893331072158254253024 = 2^5 * 3 * 1650319073869 * 448743467082178452665495095520409784795027434211306683401
1037 . 115528904868085757101698250966761985958397205888720298576829386853993456 = 2^4 * 3 * 31 * 9578651569 * 140393827859333 * 57734490065613001922702391819708499345226431
1038 . 192548174812308009005850008281205656482758736773962038786778936849937424 = 2^4 * 3 * 11 * 31 * 36473 * 4580369 * 38362720102611887 * 1835534041930821535794648296871101360297
1039 . 367607450056871344163226559143246541078296820121953003541746713485888496 = 2^4 * 3 * 11^2 * 17 * 31 * 842362576273624117 * 142576522306516388341908183152293740611449587143
1040 . 773280231597512060758513426291947499984934839199800796393662040325604368 = 2^4 * 3 * 31 * 191 * 182014885871571913 * 14948365277722592526241143135667985643529318345267
1041 . 1299596619595818710359615964667111134892726708030099977487706986844994544 = 2^4 * 3^2 * 31 * 1039 * 15131 * 33806660782490118793381 * 547770869057047907455856785713158783249
1042 . 2458655444417498478002917878888202447361634579165352522409213121755325456 = 2^4 * 3^3 * 31 * 79 * 8965390009038543814169 * 259212506923388580098398032219732848789958043
1043 . 4918463563680012192048854062754860794062670360340844438308714628683586544 = 2^4 * 3 * 31 * 3305419061612911419387670741098696770203407500229062122519297465513163
1044 . 8197439272800020320081423437924767990104450600568074063847857714472648208 = 2^4 * 3 * 19 * 31^2 * 73 * 218572384991437 * 586194623429865512819516645359676097249515156813669
1045 . 15151640610443533457428395582174705392323922919144158357946775424339137392 = 2^4 * 3 * 31^2 * 328469489473715172073976664545931004863074985239857751429647403406589
1046 . 25293464567433963110384499076694871098476226163410006291088568651921102488 = 2^3 * 3 * 19 * 31 * 16886251 * 1581495610435661 * 164911053796141581211 * 406284997838064176028497473[/code]

This is my first ever (!) escape from 2^4 * 31, and it came just nine lines after I acquired it. Even though it went straight into 2^3 * 3, that one is very easy to escape from in my experience - it is actually less persistent than the downdriver.

 10metreh 2009-10-11 08:51

Lines 667 and 670 of sequence 701184 are oddly similar:

[code] 667 . 177286387848755915467003171896178179159030958854732054743450091945986257513367907171821928041364 = 2^2 * 3^3 * 7 * 11 * 199 * 293 * 2081 * 250693 * 65331192259 * 2262270909179549267 * 4741991067576476261927654017720344624117895413853
...
670 . 2021438949074275057896853040743137850595987718393484123165484498834552307908486254143820808598636 = 2^2 * 3^2 * 7 * 11 * 47 * 163 * 2063 * 257893 * 176013952099 * 533779889413141967 * 1904293377948420261416322664999293292768947564238789[/code]

Both of them are divisible by 2^2, 3^2 (although it is 3^3 in line 667), 7 and 11. They both have prime factors between 150 and 200 (667 has an extra factor of 293 and 670 has an extra factor of 47), between 2050 and 2100, and even between 250000 and 258000 (and those two both end in 93). Above this, they have factors of 11 and 12 digits (both ending with 9), and 18 and 19 digits (both ending in 67) respectively. The large cofactors are p49 and p52.

Maybe if we looked at sequences in other bases, we'd find loads more of these...

 rodac 2009-10-11 13:01

Hello

another recreational class records

I am looking for the longest sequences who are reaching n digits
My list is uncomplete, there are certainly longer sequences fort a part of them.

an important part of them are side-sequences, and the most little are ending sequences.

If you know "better" sequences, please let me know ! :smile: I'll edit my reply, up to rectify

Reaching:
3 digits: 30 (i6)
4 digits: 138+520 (i7)
5 digits: 180 (i13)
6 digits: 138 (i23)
7 digits: 922252 (i66)
8 digits: 8844 (i119)
9 digits: 8844 (i147)
10 digits: 8844 (i209)
11 digits: 8844 (i214)
12 digits: 8844 (i216)
13 digits: 22734 (i252)
14 digits: 22734 (i258)
15 digits: 22734 (i264)
16 digits: 33552 (i616)
17 digits: 33552 (i620)
18 digits: 33552 (i623)
19 digits: 31482 (i688)
20 digits: 33552 (i807)
21 digits: 33552 (i811)
22 digits: 579480 (i936)
23 digits: 579480 (i942)
24 digits: 579480 (i947)
25 digits: 579480 (i955)
26 digits: 189948+579480 (i970)
27 digits: 579480 (987)
28 digits: 358488 (i1169)
29 digits: 358488 (i1172)
30 digits: 233280 (i1216)
31 digits: 297444 (i1438)
32 digits: 297444 (i1442)
33 digits: 297444 (i1445)
34 digits: 297444 (i1451)
35 digits: 297444 (i1463)
36 digits: 765264 (i1923)
37 digits: 765264 (i1945)
38 digits: 765264 (i1949)
39 digits: 765264 (i1952)
40 digits: 765264 (i1955)
41 digits: 765264 (i1958)
42 digits: 765264 (i1963)
43 digits: 765264 (i1967)
44 digits: 765264 (i1970)
45 digits: 765264 (i1974)
46 digits: 765264 (i1977)
47 digits: 765264 (i1980)
48 digits: 765264 (i1983)
49 digits: 765264 (i1987)
50 digits: 765264 (i1990)
51 digits: 765264 (i1993)
52 digits: 765264 (i1996)
53 digits: 763476 (i2253)
54 digits: 763476 (i3424)
55 digits: 763476 (i3428)
56 digits: 763476 (i3432)
57 digits: 731520 (i3819)
58 digits: 731520 (i3823)
59 digits: 731520 (i3826)
60 digits: 227646 (i4147)
61 digits: 227646 (i4159)
62 digits: 227646 (i4168)
63 digits: 227646 (i4178)
64 digits: 227646 (i4184)
65 digits: 227646 (i4190)
66 digits: 227646 (i4196)
67 digits: 227646 (i4205)
68 digits: 227646 (i4223)
69 digits: 227646 (i4243)
70 digits: 227646 (i4252)
71 digits: 227646 (i4262)
72 digits: 227646 (i4270)
73 digits: 227646 (i4290)
74 digits: 389508 (i4849)
75 digits: 389508 (i4862)
76 digits: 389508 (i6927)
77 digits: 389508 (i6930)
78 digits: 389508 (i6934)
79 digits: 389508 (i6938)
80 digits: 389508 (i6974)
81 digits: 389508 (i6978)
82 digits: 389508 (i6982)
83 digits: 389508 (i6985)
84 digits: 389508 (i7046)
85 digits: 389508 (i7049)
86 digits: 389508 (i7053)
87 digits: 389508 (i7067)
88 digits: 389508 (i7074)
89 digits: 314718 (i8572)
90 digits: 314718 (i8574)
91 digits: 314718 (i8577)
92 digits: 314718 (i8579)
93 digits: 314718 (i8581)
94 digits: 314718 (i8584)
95 digits: 314718 (i8586)
96 digits: 314718 (i8589)
97 digits: 314718 (i8591)
98 digits: 314718 (i8594)
99 digits: 314718 (i8596)
100 digits: 314718 (i8598)

 schickel 2009-10-17 04:46

:cool::cool::cool:

And here's the third one, at 133 digits:[code]1617. 2134390794384631128138103307530851968113625211386755303950857993760988778141536341335611817814108590056259067825205204879184058837504 = 2^9 * 3 * 11 * 23 * 31^2 * 8363 * 26725961669999161825177411960621757699 * 25570744721776150163466156594603011284449885586297345250081499429913577034186689459
1618. 4554715592545393510883800490221878991371679408645789636606399298425473469081361444258606401965259036529868527847942849313204918826496 = 2^9 * 3 * 11 * 31^2 * 15855317 * 3431934844399367027129931389745167305493 * 5155134629985305597589873038635034727381118905063583204318430511351841819211411
1619. 9123206389271434528062314811099301096595326324145346171671712648071542240085965287560573341681028925785537542968720231237632827675392 = 2^8 * 3 * 11 * 31 * 37 * 12157 * c109[/code]Turns out the 2^9 (etc.) driver is pretty darn persistent.....and very harsh, adding a digit every 3 lines or so.

 Andi47 2009-10-17 07:01

I had forgotten to post [URL="http://www.mersenneforum.org/showpost.php?p=191858&postcount=672"]this one[/URL] also here:

*very* persistent [COLOR="Red"]2[SUP]2[/SUP]*7[/COLOR] driver in sequence [URL="http://factorization.ath.cx/search.php?se=1&aq=565656&action=last20&fr=&to="]565656[/URL], lasting for *at least* 480 lines. (Several times when it was at 2[SUP]2[/SUP]*7[SUP]2[/SUP] or 2[SUP]2[/SUP]*7[SUP]3[/SUP], it failed to escape the driver and went back to 2[SUP]2[/SUP]*7.)

 Batalov 2009-10-18 21:46

Yet another steep(-est) sequence? :smile:
[URL]http://factordb.com/aliquot.php?type=1&aq=707778[/URL]

 schickel 2009-10-29 05:29

My hardest downdriver start ever (starting at line 1023 in 29772):[code]c133 = 2^2 * 167 * p65 * p66 (!)
c133 = 2^2 * p132
c133 = 2 * 5 * 47 * p60 * p70 (!)
c133 = 2 * 617 * p39 * p41 * p50[/code]Luckily, the p39 came out via ECM. Line 1032, however, is currently running NFS on a c122.... :cry:

 10metreh 2009-10-29 07:59

[QUOTE=schickel;194149]My hardest downdriver start ever (starting at line 1023 in 29772):[code]c133 = 2^2 * 167 * p65 * p66 (!)
c133 = 2^2 * p132
c133 = 2 * 5 * 47 * p60 * p70 (!)
c133 = 2 * 617 * p39 * p41 * p50[/code]Luckily, the p39 came out via ECM. Line 1032, however, is currently running NFS on a c122.... :cry:[/QUOTE]

Glad to hear that all those months of work on 29772 have paid off :smile:

 schickel 2009-10-30 00:04

[QUOTE=10metreh;194158]Glad to hear that all those [strike]months[/strike] [B]years[/B] of work on 29772 have paid off :smile:[/QUOTE]Actually, I started work on 29772 on or around 8/9/07 at this point:[code]29772 714. 2^3 * 3^3 C99 sz 104[/code]and have been working on it steadily, except for short time outs while resolving downdriver runs on other sequences....

That's why I started the "[strike]Released[/strike] [color=blue]Retired[/color] sequences" thread originally, I envisioned people spending more time on sequences at higher levels.

 gd_barnes 2009-10-31 06:16

[quote=Batalov;193198]Yet another steep(-est) sequence? :smile:
[URL]http://factordb.com/aliquot.php?type=1&aq=707778[/URL][/quote]

Got you beat handily with 210222 [URL="http://factorization.ath.cx/search.php?se=1&aq=210222&action=last20&fr=&to"]here[/URL]. It hits 107 digits at i=292 vs. your i=296. :smile: Although, I am going to guess that 707778 may beat (or at least tie) 210222 to 110 digits. 707778 has the terrible 2^3*3*5 driver vs. 210222 that has various unstable guides of 2^2*3, 2^2*3^2, 2^2*3^3, 2^3*3, etc. so 707778 is increasing more rapidly at the moment.

One that was increasing more rapidly at the same time that 707778 was and is probably a better one is 111624 [URL="http://factorization.ath.cx/search.php?se=1&aq=111624&action=range&fr=275&to"]here[/URL]. It hits 107 digits at i=295 to still best 707778 by a single index but still had the horrific 2^5*3*7 driver combined with a consistent factor of 5 to hit 110 digits at an astounding i=303. I continued with 111624 because I never got a hard C>100 until it hit size 114. By that time, "unfortunately" it had dropped the nasty driver in favor of the slowly increasing 2*3 driver.

Therefore, I will claim the following records:
To 110 digits: 111624 at i=303
To 107 digits: 210222 at i=292

That is until someone comes along with a better record. Can anyone top these? :smile:

It is possible that 210222 may hit 110 digits faster due to the unstable guides that could become a driver at any point but it appears doubtful. I had to stop with it at size 107 with a hard C106 at i=295.

Analysis: At their respective current rates of increase, 210222 and 707778 appear that they would only hit size 109 by i=303. Therefore I think that 111624 is the standard to beat to 110 digits. If you have the resources, those two might be interesting to take to at least 110 digits.

I knew advancing some of those sequences from the "shortest sequences" list might prove useful at some point. :smile:

Gary

All times are UTC. The time now is 16:25.